Heat Transfer Concept Page - 10

Result

Effect of impurities on boiling point

Boiling point of a liquid increases with addition of impurities in it. Hence, cooking is better when salt is added to the water.

Definition

Crystallization and its examples

Crystallization is the way that atoms gather to make tightly bonded or connected groups. It separates a solid from a liquid or sometimes from a gas. Crystallization can be from a melt or from a solution, and can be natural or artificial. 
Artificial crystallization is a technique that forms solid crystals from a homogeneous solution.For crystallization to occur the solution at hand ought to be supersaturated. This can be achieved by solvent evaporation, cooling, chemical reaction, 'drowning' being the most common ones used in industrial practice. 
Protein Crystallization:
The solubility of protein molecules is subject to many factors, especially the interaction with other compounds in solution. Most proteins are soluble at physiological conditions, but as the concentration of solutes rises, the protein becomes less soluble, driving it to crystallize or precipitate. This phenomenon is known as "salting out". Counter-intuitively, at very low solute concentrations, proteins also become less soluble, because some solutes are necessary for the protein to remain in solution. This converse phenomenon is known as "salting in". Most protein crystallization techniques form crystals by salting out the protein into crystals, although some experimental setups can produce crystals using the salting in effect. Due to the molecular variations between individual proteins, conditions unique to each protein must be obtained for a successful crystallization. Therefore, attempting to crystallize a protein without a proven protocol can be very challenging and time consuming.

Definition

Specific latent heat

Latent heat is the amount of heat energy absorbed (or released) in change of phase of the material. Temperature is constant in the process.
Specific latent heat of a substance is the amount of heat energy absorbed (or released) to change the phase of unit mass of substance.
L=Qm$L={\displaystyle \frac{Q}{m}}$

Definition

Latent heat of fusion

The amount of heat required for a solid-liquid state change is called the latent heat of fusion. Its units are J/g and cal/g.

Definition

Latent heat of vaporisation

The amount of heat required for a liquid-gas state change is called latent heat of vaporization. Values are usually quoted in J/mol or kJ/mol (molar enthalpy of vaporization), although kJ/kg or J/g (specific heat of vaporization), and older units like kcal/mol, cal/g and Btu/lb are sometimes still used, among others.

Diagram

Heating curve of ice

Heating curve of ice is shown in the attached graph. It is assumed that heat is supplied at a constant rate.
First phase: Ice at temperature <0o C$<0^{o}C$ to ice at 0o C$0^{o}C$
Second phase: Ice at 0o C$0^{o}C$ to water at 0o C$0^{o}C$.
Third phase: Water at 0o C$0^{o}C$ to water at temperature >0o C$>0^{o}C$

Definition

Specific latent heat of some substances

Substance	Specific latent heat of fusion(kJKg−1$kJK{g}^{-1}$)	Specific latent heat of vaporisation(kJKg−1$kJK{g}^{-1}$)
Ice(water)	334	2258
Mercury	11	294
Oxygen	14	213

Example

High specific latent heat of fusion of ice

Some natural consequences of high specific latent heat of fusion of ice are:

• Snow on mountains melt slowly.
• Lakes and ponds in cold countries freezes slowly.
• Drinks cool faster on addition of ice.

Definition

Specific latent heat of vaporization of water

Mass of the calorimeter = m1$m_1$
Mass of the water = m2$m_2$
Mass of the condensed steam = m3$m_3$
Temperature of the steam = θ1$\theta 1$
Initial temperature of water in the calorimeter = θ2$\theta 2$
Final temperature of water in the calorimeter = θ3$\theta 3$
Specific latent heat of vaporization of water = L$L$
Specific heat capacity of the material of the calorimeter = s1$s_1$
Specific heat capacity of water = s2$s_2$
Heat gained by the calorimeter = m1s1(θ3−θ2)$m_1{s}_1({\theta }_3-{\theta }_2)$
Heat gained by the water kept initially in the calorimeter = m2s2(θ3−θ2)$m_2{s}_2({\theta }_3-{\theta }_2)$
Heat lost by the steam in condensing = m3L$m_{3}L$
Heat lost by the condensed water in cooling from temperature θ1${\theta }_1$ to θ3${\theta }_3$ = m3s2(θ1−θ3)$m_3{s}_2({\theta }_1-{\theta }_3)$
Assuming no heat loss to the surrounding 
m1s1(θ3−θ2)+m2s2(θ3−θ2)=m3L+m3s2(θ1−θ3)$m_1{s}_1({\theta }_3-{\theta }_2)+m_2{s}_2({\theta }_3-{\theta }_2)=m_{3}L+m_3{s}_2({\theta }_1-{\theta }_3)$
L=m1s1(θ3−θ2)+m2s2(θ3−θ2)m3−s2(θ1−θ3)$L={\displaystyle \frac{m_1{s}_1({\theta }_3-{\theta }_2)+m_2{s}_2({\theta }_3-{\theta }_2)}{m_3}}-s_2({\theta }_1-{\theta }_3)$

Diagram

Heating(solid to liquid) and cooling(liquid to solid) curve for naphthalene

Heating and cooling curves of naphthalene is attached in the figure. Note that freezing point of naphthalene is 80o C${80}^{o}C$.

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